Thermal conductivity of a weakly interacting Bose gas in quasi-one-dimension

Abstract

Transport coefficients are typically divergent for quantum integrable systems in one dimension, such as a Bose gas with a two-body contact interaction. However, when a one-dimensional system is realized by confining bosons into a tight matter waveguide, an effective three-body interaction inevitably arises as leading perturbation to break the integrability. This fact motivates us to study the thermal conductivity of a Bose gas in one dimension with both two-body and three-body interactions. In particular, we evaluate the Kubo formula exactly to the lowest order in perturbation by summing up all contributions that are naively higher orders in perturbation but become comparable in the zero-frequency limit due to the pinch singularity. Consequently, a self-consistent equation for a vertex function is derived, showing that the thermal conductivity in quasi-one-dimension is dominated by the three-body interaction rather than the two-body interaction. Furthermore, the resulting thermal conductivity in the weak-coupling limit proves to be identical to that computed based on the quantum Boltzmann equation and its temperature dependence is numerically determined.

12 pages, 7 figures; published version with appendix added

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Heat Transport in low-dimensional systems
• Viscosity and scale invariance in the unitary Fermi gas
• Breakdown of integrability in a quasi-one-dimensional ultracold bosonic gas
• Friction and diffusion of matter-wave bright solitons
• Relaxation of a high-energy quasiparticle in a one-dimensional Bose gas
• Renormalized Linear Kinetic Theory as Derived from Quantum Field Theory - a novel diagrammatic method for computing transport coefficients -
• Thermal Transport in One Dimensional Electronic Fluid
• Hydrodynamic Relaxation in a Strongly Interacting Fermi Gas
• Microscopic derivation of the Boltzmann equation for transport coefficients of resonating fermions at high temperature
• Bulk viscosity of dual Bose and Fermi gases in one dimension

Cited by in corpus (5)

• Three-body forces and Efimov physics in nuclei and atoms
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Viscous Drude weight of dual Bose and Fermi gases in one dimension